Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2344)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃>=-5/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=-5/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=-5/2, b₁=1/2

http://functions.wolfram.com/07.27.03.2344.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), -(5/2)}, {1/2, 3/2}, z] == (175 (15 Pi^2 Sqrt[-z] + 60 Pi^2 (-z)^(3/2) + 8 Pi^2 (-z)^(5/2)))/8192 + (Sqrt[1 - z] (95679 - 2095298 z + 941264 z^2 - 1200 z^3))/98304 - (35 (-25 + 3300 z + 12000 z^2 - 5184 z^3) Log[Sqrt[1 - z] + Sqrt[-z]])/ (32768 Sqrt[-z]) - (525 (15 Sqrt[-z] + 60 (-z)^(3/2) + 8 (-z)^(5/2)) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/4096 + (525 (15 Sqrt[-z] + 60 (-z)^(3/2) + 8 (-z)^(5/2)) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/2048 + (525 (15 Sqrt[-z] + 60 (-z)^(3/2) + 8 (-z)^(5/2)) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/2048 - (525 (15 Sqrt[-z] + 60 (-z)^(3/2) + 8 (-z)^(5/2)) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/2048

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]